Propagation Of SH Surface Wave Tuned By Locally Resonant Metasurface In Piezoelectric Layered Half-Space Structures

A locally resonant meta-surface is a periodic array of sub-wavelength locally resonant unit such as spring-mass resonators on the surface of an elastic substrate/ halfspace.When a surface wave propagating along the surface and meeting such array on its propagation path,some extraordinary wave phenomena will occur,which are different from the classical surface waves on a smooth and flat free surface of an elastic half-space.A locally resonant meta-surface can be used to tune the propagation of surface waves by controlling the strength of the interaction between the surface waves and the resonant array.In this thesis,we extend an elastic solid to a piezoelectric(PE)solid.By using the effective medium approach,the tuning of BG wave on a PE half-space,as well as Love waves in an elastic layer over a PE half-space and its inverse configuration are investigated theoretically by a locally resonant meta-surface.For the three kinds of meta-surface described above,dispersion equations of the two kinds of SH-type surface waves are derived,respectively.A dimensionless parameter F,which controls the interaction strength between surface waves and the resonant arrays is defined.The tuning of SH-type surface wave by the locally resonant meta-surface is discussed.Owing to electro-mechanical coupling effect of PE material,the BG/Love waves in the three kinds of meta-surface exhibit novel propagation behaviors different from those of the classical BG/Love waves in the corresponding configuration without the resonant arrays.The main conclusions are as follows.First of all,the first low-frequency guided mode of BG/Love waves appear below the resonant frequency,which shows a wave slowing effect as the wave number increases.With the increase of the wave number,the frequency of the first mode tends to the resonant frequency in which the meta-surface seems as a resonator vibrating.The second and the other higher modes appear above the resonant frequency with their frequencies higher than the corresponding modes of the classical BG/Love waves.Furthermore,an “avoided crossing band gap” appears between the first and the second modes near the resonant frequency.By tuning the parameter F which controls the interaction strength between the resonators and BG/Love waves,the dispersion curves and the width of the band gap can be tuned.As F increases,the frequencies of the higher modes and the width of band gap increase while the frequency of the first mode decreases.By tuning the parameter F,the values and wave mode shapes of the displacement,electrical potential and stresses can be tuned.Compared with the elastic/PE layered meta-surface,the PE meta-surface and PE/elastic layered metasurface are easier to produce an avoiding crossing band gap.In addition,the PE metasurface and the PE/elastic layered meta-surface are easier to obtain wider band gaps by tuning F than the elastic/PE layered meta-surface.This work will provide a theoretical guide for the design and application of the newly acoustic surface wave devices which are based on the configuration and function of the locally resonant piezoelectric layered meta-surface.